Analog Integrated Circuits and Signal Processing

, Volume 101, Issue 3, pp 489–512 | Cite as

The effects of symmetry breaking on the dynamics of a simple autonomous jerk circuit

  • Leandre Kamdjeu Kengne
  • Jacques KengneEmail author
  • Hilaire Bertrand Fotsin


We investigate the dynamics of a simple jerk circuit where the symmetry is broken by forcing a dc voltage. The analysis shows that with a zero forcing dc voltage, the system displays a perfect symmetry and develops rich dynamics including period doubling, merging crisis, hysteresis, and coexisting multiple (up to six) symmetric attractors. In the presence of a non-zero forcing dc voltage, several unusual and striking nonlinear phenomena occur such as coexisting bifurcation branches, hysteresis, asymmetric double scroll strange attractors, and multiple coexisting asymmetric attractors for some appropriate sets of system parameters. In the latter case, different combinations of attractors are depicted consisting for instance of two, three, four, or five disconnected periodic and chaotic attractors depending solely on the choice of initial conditions. The investigations are carried out by using standard nonlinear analysis tools such as Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase space trajectory plots. The theoretical results are checked experimentally and a very good agreement is found between theory and experiment.


Jerk circuit with broken symmetry Dynamic analysis Coexisting multiple attractors Basins of attraction Experimental study 



The authors would like to thank the anonymous reviewers whose criticisms and suggestions have helped to considerably improve the quality and content of this manuscript.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Leandre Kamdjeu Kengne
    • 1
    • 2
  • Jacques Kengne
    • 1
    Email author
  • Hilaire Bertrand Fotsin
    • 1
    • 2
  1. 1.Laboratoire d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV BandjounUniversity of DschangDschangCameroon
  2. 2.Laboratory of Electronics and Signal Processing, Department of PhysicsUniversity of DschangDschangCameroon

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